Question

.. questions no.16..thanks for your help

Answer 1

Step-by-step explanation:

Construction: Join OP.

Proof: In triangles OPQ and OPM we have,

OP = OP                                         [Side Common to both triangles]

PM = PQ                                         [Given in the question]

angle Q = angle M                         [Both equal to 90 deg.]

By RHS congruence criteria

triangles OPQ is congruent to OPM

Angle QOP = Angle MOP

OP is the bisector of angle QOM.

Hence proved that P lies on bisector of Angle AOB.

Answer 2

Step-by-step explanation:

Construction: Join OP.

Proof: In triangles OPQ and OPM we have,

OP = OP                                         [Side Common to both triangles]

PM = PQ                                         [Given in the question]

angle Q = angle M                         [Both equal to 90 deg.]

By RHS congruence criteria

triangles OPQ is congruent to OPM

Angle QOP = Angle MOP

OP is the bisector of angle QOM.

Hence proved that P lies on bisector of Angle AOB.